Step by step Gauss-Jordan reduction of a matrix

15.7.5 Step by step Gauss-Jordan reduction of a matrix

One step of Gauss-Jordan elimination involves taking a non-zero element of a matrix (the pivot) and adding multiples of its row to the other rows to get zeros above and below the pivot. The pivot command performs this operation.

pivot takes three arguments:
- A, a a matrix with n rows and p columns.
- l and c, two integers such that l is the index of a row of A and c is an index of column of A, and the element of A in row l and column c is non-zero.
pivot(A,l,c) returns the result of performing one step of the Gauss-Jordan method using the element of A in row l, column c as pivot.

Examples

pivot([[1,2],[3,4],[5,6]],1,1)

⎡
⎢
⎢
⎣

−2	0
3	4
2	0

⎤
⎥
⎥
⎦

pivot([[1,2],[3,4],[5,6]],0,1)

⎡
⎢
⎢
⎣

1	2
2	0
4	0

⎤
⎥
⎥
⎦